Question

How do you solve the systems \[3x+3y=-9\] and \[3x-3y=21\]?

Answer 1

Hint: In this problem, we have to solve the given system of equations to find the value of x and y. Here we can see that, we already have similar terms to be cancelled. We can use elimination methods to cancel similar terms. But here both the terms with two unknown variables are similar and we can add/subtract the equations to get anyone of the unknown variable value and substitute in one of the equations to get the other value.

Complete step by step solution:
We know that the given system of equations to be solved are,
\[3x+3y=-9\] ……… (1)
\[3x-3y=21\] …….. (2)
We can now subtract the equation by elimination method.
We should know that to solve by elimination method, we should have similar terms to be cancelled.
Now we can subtract the above equations (1) and (2), we get
\[\begin{align}
  & \Rightarrow 3x+3y+9-\left( 3x-3y-21 \right)=0 \\
 & \Rightarrow 3x+3y+9-3x+3y+21=0 \\
\end{align}\]
Now we can cancel similar terms and simplify, we get
\[\begin{align}
  & \Rightarrow 3y+3y+21+9=0 \\
 & \Rightarrow 6y=-30 \\
 & \Rightarrow y=-5 \\
\end{align}\]
Therefore, the value of y is -5.
Now we can substitute the y value in equation (1), we get
\[\begin{align}
  & \Rightarrow 3x+3\left( -5 \right)=-9 \\
 & \Rightarrow 3x=6 \\
 & \Rightarrow x=2 \\
\end{align}\]

Therefore, the value of x = 2 and y = -5.

Note: Students make mistakes while multiplying the correct number to the equations for the similar terms to be cancelled. But here we already have similar terms to be cancelled, so we can proceed by adding/subtracting the terms to cancel similar terms to get one unknown variable value and substitute it in any equation to get the other. We can verify the values we found for whether it is correct. We can substitute the values in any of the equations.
When x = 2 and y = -5 in \[3x+3y=-9\].
\[\begin{align}
  & \Rightarrow 3\left( 2 \right)+3\left( -5 \right)=-9 \\
 & \Rightarrow 6-15=-9 \\
\end{align}\]
Therefore, the values x = 2 and y = -5 are correct.